The Growth Ratio of Synchronous Rational Relations is Unique

Olivier Carton


Abstract

We introduce $\alpha$-synchronous relations for a rational number~$\alpha$. We show that if a rational relation is both $\alpha$- and $\alpha'$-synchronous for two different numbers $\alpha$ and~$\alpha'$, then it is recognizable. We give a synchronization algorithm for $\alpha$-synchronous transducers. We also prove the closure under boolean operations and composition of $\alpha$-synchronous relations.


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